GATE | GATE-CS-2004 | Question 70

The following propositional statement is
(P → (Q v R)) → ((P ^ Q) → R)
(A) satisfiable but not valid
(B) valid
(C) a contradiction
(D) none of the above


Answer: (A)

Explanation: We create the truth table for given statement S as :

2004-70

A formula is satisfiable if there is atleast one assignment for which it is true. Clearly this formula is satisfiable as there are 7 assignments for which it is true.
A formula is valid if it is true for all assignments, which is not the case here.
Thus, option (A) is correct.

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